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First release of PowerSAS.m
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Rui Yao
248
internal/integ.m
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248
internal/integ.m
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function dx=integ(SysData,SysPara,xt,dt)
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% [INTERNAL] Perform an integration
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% Author: Rui Yao <ruiyao@ieee.org>
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%
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% Copyright (C) 2021, UChicago Argonne, LLC. All rights reserved.
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%
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% OPEN SOURCE LICENSE
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%
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% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
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%
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% 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
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% 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
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% 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
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%
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%
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% ******************************************************************************************************
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% DISCLAIMER
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%
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% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
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% WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
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% PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
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% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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% PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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% CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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% ***************************************************************************************************
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%
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% FUNCTION integ
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% CAUTION: this function is used internally. Do not call it directly unless you know what you are doing.
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%
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% INPUT
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% SysData - System data for simulation
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% SysPara - Parameters representing the events happening in the system
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% xt - Initial state
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% dt - Time step length
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%
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% OUTPUT
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% dx - Incremental of the system state
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%
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%
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[bus,sw,pv,pq,shunt,line,ind,zip,syn,exc,tg,agc,cac,cluster]=unfoldSysData(SysData);
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[nState,idxs]...
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=getIndexDyn(SysData);
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[V,Q,s,d,w,eq1,eq2,ed1,ed2,psid,psiq,Pg,Ef,Vavrm,Vavrr,Vavrf,Vavrref,tgovg,tgovm,tgovmech,f,dpg,qplt,vg]=unfoldX(xt,SysData);
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nbus=size(bus,1);
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[nIslands,islands,refs]=searchIslands(bus(:,1),line(:,1:2));
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% Determine the frequency model of each island
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freqTypeTag=zeros(nIslands,1);%0:sw,1:syn,2:steady-state f
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freqKeptTag=zeros(nbus,1);
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frefs=refs;
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fswTag=zeros(nbus,1);
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fsynTag=zeros(nbus,1);
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fswTag(sw(:,1))=1;
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fswTagxD=fswTag;
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fsynTag(syn(:,1))=1;
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D0=imag(V);
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for isl=1:nIslands
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if isempty(find(fswTag(islands==isl)==1, 1))
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if isempty(find(fsynTag(islands==isl)==1, 1))
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freqTypeTag(isl)=2;
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busesInIsland=find(islands==isl);
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[~,imin]=min(abs(D0(busesInIsland)));
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frefs(isl)=busesInIsland(imin(1));
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fswTagxD(frefs(isl))=1;
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freqKeptTag(busesInIsland)=1;
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else
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freqTypeTag(isl)=1;
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end
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end
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end
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freqKeptTagxRef=freqKeptTag;
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freqKeptTagxRef(frefs)=0;
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nFreqKept=sum(freqKeptTag);
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pVec=zeros(nbus,1);
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qVec=zeros(nbus,1);
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pVec(pq(:,1))=pVec(pq(:,1))+pq(:,4);
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qVec(pq(:,1))=qVec(pq(:,1))+pq(:,5);
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if ~isempty(zip)%zipMode=0, account for the PQ components in ZIP loads
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pVec=pVec+accumarray(zip(:,1),zip(:,7).*zip(:,12),[nbus,1]);
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qVec=qVec+accumarray(zip(:,1),zip(:,10).*zip(:,12),[nbus,1]);
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end
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SVec=pVec+1j*qVec;
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[Ig,Im,Ii,Is]=calcCurrent(xt,syn,ind,zip,SVec,idxs.vIdx,idxs.sIdx,idxs.deltaIdx,idxs.omegaIdx,idxs.eq1Idx,idxs.eq2Idx,idxs.ed1Idx,idxs.ed2Idx,idxs.psidIdx,idxs.psiqIdx,idxs.efIdx);
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[pqIncr,pvIncr,Rind0,Rind1,Reind0,Reind1,Rzip0,Rzip1,Ytr0,Ytr1,Ysh0,Ysh1,~,~,~,~,~,Tmech1,Varref1,Ef1,Pm1,Eq11]=unfoldSysPara(SysPara);
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%
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dx=zeros(size(xt));
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%
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% d=xt(deltaIdx);
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% w=xt(omegaIdx);
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% eq1=xt(eq1Idx);
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% eq2=xt(eq2Idx);
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% ed1=xt(ed1Idx);
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% ed2=xt(ed2Idx);
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% psid=xt(psidIdx);
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% psiq=xt(psiqIdx);
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% V=xt(vIdx);
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% s=xt(sIdx);
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if ~isempty(ind)
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nInd=size(ind,1);
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indIdx=ind(:,1);
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Zm1=ind(:,7)+1j*ind(:,8);
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Rm2=ind(:,9);
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Xm2=ind(:,10);
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Zmm=1j*ind(:,13);
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Tm0=ind(:,15)+ind(:,16)+ind(:,17);
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Tm1=-ind(:,16)-2*ind(:,17);
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Tm2=ind(:,17);
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Hm=ind(:,14);
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end
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nSyn=size(syn,1);
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if ~isempty(syn)
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synIdx=syn(:,1);
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Igx=real(Ig);
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Igy=imag(Ig);
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Igd=Igx.*sin(d)-Igy.*cos(d);
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Igq=Igx.*cos(d)+Igy.*sin(d);
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Vgx=real(V(synIdx));
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Vgy=imag(V(synIdx));
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Vgd=Vgx.*sin(d)-Vgy.*cos(d);
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Vgq=Vgx.*cos(d)+Vgy.*sin(d);
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wgb=syn(:,4);
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model=syn(:,5);
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Xgl=syn(:,6);
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Rga=syn(:,7);
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Xgd=syn(:,8);
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Xgd1=syn(:,9);
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Xgd2=syn(:,10);
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Tgd1=syn(:,11);
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Tgd2=syn(:,12);
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Xgq=syn(:,13);
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Xgq1=syn(:,14);
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Xgq2=syn(:,15);
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Tgq1=syn(:,16);
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Tgq2=syn(:,17);
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Mg=syn(:,18);
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Dg=syn(:,19);
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TgAA=syn(:,24);
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gammad=Tgd2./Tgd1.*Xgd2./Xgd1.*(Xgd-Xgd1);
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gammaq=Tgq2./Tgq1.*Xgq2./Xgq1.*(Xgq-Xgq1);
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Pe=Vgq.*Igq+Vgd.*Igd+Rga.*(Igq.*Igq+Igd.*Igd);
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for i=1:nSyn
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if model(i)==8
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dx(idxs.deltaIdx(i))=wgb(i)*w(i)*dt;
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dx(idxs.omegaIdx(i))=(Pg(i)-Pe(i)-Dg(i)*w(i))/Mg(i)*dt;
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dx(idxs.psidIdx(i))=wgb(i)*(Rga(i)*Igd(i)+psiq(i)+Vgd(i))*dt;
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dx(idxs.psiqIdx(i))=wgb(i)*(Rga(i)*Igq(i)-psid(i)+Vgq(i))*dt;
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dx(idxs.eq1Idx(i))=(-eq1(i)-(Xgd(i)-Xgd1(i)-gammad(i))*Igd(i)+(1-TgAA(i)/Tgd1(i))*Ef(i))/Tgd1(i)*dt;
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dx(idxs.ed1Idx(i))=(-ed1(i)+(Xgq(i)-Xgq1(i)-gammaq(i))*Igq(i))/Tgq1(i)*dt;
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dx(idxs.eq2Idx(i))=(-eq2(i)+eq1(i)-(Xgd1(i)-Xgd2(i)+gammad(i))*Igd(i)+TgAA(i)/Tgd1(i)*Ef(i))/Tgd2(i)*dt;
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dx(idxs.ed2Idx(i))=(-ed2(i)+ed1(i)+(Xgq1(i)-Xgq2(i)+gammaq(i))*Igq(i))/Tgq2(i)*dt;
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elseif model(i)==6
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dx(idxs.deltaIdx(i))=wgb(i)*w(i)*dt;
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dx(idxs.omegaIdx(i))=(Pg(i)-Pe(i)-Dg(i)*w(i))/Mg(i)*dt;
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dx(idxs.eq1Idx(i))=(-eq1(i)-(Xgd(i)-Xgd1(i)-gammad(i))*Igd(i)+(1-TgAA(i)/Tgd1(i))*Ef(i))/Tgd1(i)*dt;
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dx(idxs.ed1Idx(i))=(-ed1(i)+(Xgq(i)-Xgq1(i)-gammaq(i))*Igq(i))/Tgq1(i)*dt;
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dx(idxs.eq2Idx(i))=(-eq2(i)+eq1(i)-(Xgd1(i)-Xgd2(i)+gammad(i))*Igd(i)+TgAA(i)/Tgd1(i)*Ef(i))/Tgd2(i)*dt;
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dx(idxs.ed2Idx(i))=(-ed2(i)+ed1(i)+(Xgq1(i)-Xgq2(i)+gammaq(i))*Igq(i))/Tgq2(i)*dt;
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elseif model(i)==5
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dx(idxs.deltaIdx(i))=wgb(i)*w(i)*dt;
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dx(idxs.omegaIdx(i))=(Pg(i)-Pe(i)-Dg(i)*w(i))/Mg(i)*dt;
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dx(idxs.eq1Idx(i))=(-eq1(i)-(Xgd(i)-Xgd1(i)-gammad(i))*Igd(i)+(1-TgAA(i)/Tgd1(i))*Ef(i))/Tgd1(i)*dt;
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dx(idxs.eq2Idx(i))=(-eq2(i)+eq1(i)-(Xgd1(i)-Xgd2(i)+gammad(i))*Igd(i)+TgAA(i)/Tgd1(i)*Ef(i))/Tgd2(i)*dt;
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dx(idxs.ed2Idx(i))=(-ed2(i)+(Xgq(i)-Xgq2(i))*Igq(i))/Tgq2(i)*dt;
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elseif model(i)==4
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dx(idxs.deltaIdx(i))=wgb(i)*w(i)*dt;
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dx(idxs.omegaIdx(i))=(Pg(i)-Pe(i)-Dg(i)*w(i))/Mg(i)*dt;
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dx(idxs.eq1Idx(i))=(-eq1(i)-(Xgd(i)-Xgd1(i))*Igd(i)+Ef(i))/Tgd1(i)*dt;
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dx(idxs.ed1Idx(i))=(-ed1(i)+(Xgq(i)-Xgq1(i))*Igq(i))/Tgq1(i)*dt;
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elseif model(i)==3
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dx(idxs.deltaIdx(i))=wgb(i)*w(i)*dt;
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dx(idxs.omegaIdx(i))=(Pg(i)-Pe(i)-Dg(i)*w(i))/Mg(i)*dt;
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dx(idxs.eq1Idx(i))=(-eq1(i)-(Xgd(i)-Xgd1(i))*Igd(i)+Ef(i))/Tgd1(i)*dt;
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elseif model(i)==2
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dx(idxs.deltaIdx(i))=wgb(i)*w(i)*dt;
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dx(idxs.omegaIdx(i))=(Pg(i)-Pe(i)-Dg(i)*w(i))/Mg(i)*dt;
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% dx(eq1Idx(i))=Eq11(i)*dt;
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end
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end
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dx(idxs.efIdx)=Ef1*dt;
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dx(idxs.pgIdx)=Pm1*dt;
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end
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if ~isempty(ind)
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yind=1./(Zm1+Zmm.*(Rm2+1j*Xm2.*s)./(Rm2+s.*(Zmm+1j*Xm2)));
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il=V(indIdx).*yind;
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ir=il-(V(indIdx)-il.*Zm1)./Zmm;
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dx(idxs.sIdx)=dt*((Tm0+Tm1.*s+Tm2.*s.*s)-ir.*conj(ir).*Rm2./s)/2./Hm;
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end
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Vmag=abs(V);
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if ~isempty(exc)
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excIdx=exc(:,1);
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VavrMax=exc(:,3);
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VavrMin=exc(:,4);
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muavr0=exc(:,5);
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Tavr1=exc(:,7);
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Tavr2=exc(:,6);
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vavrf0=exc(:,8);
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Vavr0=exc(:,9);
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Tavre=exc(:,10);
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Tavrr=exc(:,11);
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VmagAvr=Vmag(synIdx(excIdx));
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dx(idxs.vavrmIdx)=(VmagAvr-Vavrm)./Tavrr*dt;
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dx(idxs.vavrrIdx)=(muavr0.*(1-Tavr1./Tavr2).*(Vavrref-Vavrm)-Vavrr)./Tavr2*dt;
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dx(idxs.vavrfIdx)=((Vavrr+muavr0.*Tavr1./Tavr2.*(Vavrref-Vavrm)+vavrf0).*VmagAvr./Vavr0-Vavrf)./Tavre*dt;
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dx(idxs.vavrrefIdx)=Varref1*dt;
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end
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%TODO: AGC model
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if ~isempty(tg)
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tgIdx=tg(:,1);
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wtgref=tg(:,3);
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Rtg=tg(:,4);
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Ttgmax=tg(:,5);
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Ttgmin=tg(:,6);
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Ttg2=tg(:,7);
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Ttg1=tg(:,8);
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dx(idxs.tgovgIdx)=((1-Ttg1./Ttg2).*(wtgref-w(tgIdx))./Rtg-tgovg)./Ttg2*dt;
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dx(idxs.tmechIdx)=Tmech1*dt;
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end
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nTg=size(tg,1);
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fx=zeros(nbus,1);
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synTag=zeros(nbus,1);
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synTag(syn(:,1))=1:nSyn;
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numSynOnBus=accumarray(syn(:,1),1,[nbus,1]);
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if ~isempty(agc)
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agcExt=zeros(nbus,size(agc,2));
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agcExt(agc(:,1),:)=agc;
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dx(idxs.dpgIdx)=-f.*agcExt(:,4)*dt;
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dx(idxs.tmechIdx)=dx(idxs.tmechIdx)+dx(idxs.dpgIdx(syn(tg(:,1),1)));
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dx(idxs.pgIdx)=dx(idxs.pgIdx)+dx(idxs.dpgIdx(syn(:,1)));
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end
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end
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